Question

Please help

-) A garden's length is 6m greater than its width.
The area of the garden is 720 m²
What is the length of the garden?
​

Answer 1

Length of garden will be 30 metres.

Explanation:

Let the Width of garden be x metres.

then,

Length of garden will be (x+6) metres.

Area = Length × Breadth

720 = x X (c+6)

720 = x²+6x

0 = x²+6x-720

As we can see above equation is a quadratic equation in the form of ax²+bx+C.

so,

`= \frac{ - b ± \sqrt{{b}^(2) - 4ac} }{2a} \\ = \frac{ - 6 ± \sqrt{{6}^(2) - 4 * 1 * - 720} }{2} \\ = ( - 6 ± √(36 + 2880) )/(2) \\ = ( - 6 ± √(2916) )/(2) \\ = ( - 6 ± 54)/(2)\\= (-6+54)/(2) ... ( - 6 - 54)/(2) \\ = (48)/(2) ... ( - 60)/(2) \\ = 24... - 30`

One of the Roots of the Quadratic equation is 24 and other is -30.

And as we know width of any garden cannot be negative so the width of garden will be 24 metres.

As we got the width,

adding 6 to it will give us the Length,

So,

24 metres + 6 = 30 metres.

Length of the garden is 30 metres.

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